Question

Find the roots of the following equations, if they exist, by applying the quadratic formula:

√3x² + 10x - 8√3 = 0

Answer 1

Given

√3x² + 10x - 8√3 = 0

On comparing it with ax² + bx + x = 0, we get

a = √3, b = 10 and c = -8√3

Discriminant D is given by:

D = (b² - 4ac)

= (10)² - 4 x √3 x (-8√3)

= 100 + 96

= 196 > 0

Hence, the roots of the equation are real. 

Roots α and β are given by:

Thus, the roots of the equation are \(\frac{2\sqrt3}3\) and \(-4\sqrt3\)